Value Iteration (VI) is one of the most classic algorithms for solving Markov Decision Processes (MDPs), which lays the foundations for various more advanced reinforcement learning algorithms, such as Q-learning. VI may take a large number of iterations to converge as it is a first-order method. In this paper, we introduce the Newton Value Iteration (NVI) algorithm, which eliminates the impact of action space dimension compared to some previous second-order methods. Consequently, NVI can efficiently handle MDPs with large action spaces. Building upon NVI, we propose a novel approach called Sketched Newton Value Iteration (SNVI) to tackle MDPs with both large state and action spaces. SNVI not only inherits the stability and fast convergence advantages of second-order algorithms, but also significantly reduces computational complexity, making it highly scalable. Extensive experiments demonstrate the superiority of our algorithms over traditional VI and previously proposed second-order VI algorithms.

Sketched Newton Value Iteration for Large-Scale Markov Decision Processes

Main Track - Machine Learning

technical paper

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Jinsong Liu

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Sketched Newton Value Iteration for Large-Scale Markov Decision Processes

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